Jon Begins jogging at a steady 3 m/sec down the middle of lane one of a straight track. Laura starts even with him in the cneter of lane two but moves at 4 m.sec. At the instant they begin, Ellis is loacted 100 meters down the track in lane four, and is heading towards them in his at 6 m.sec. After how many seconds will the runners lie in a straight line?

a) Let t be the number of seconds the three have been running. Write expressions for the number of meters each has run after t seconds.

b) Consider the location of each runner as a point on a graph. What quantity might you use as the x-coordinate? What quantity might you use as the x-coordinate? What quantity might you use as the y-coordinate?

c) How can you tell if three points are on a line? Use this to solve the problem.

The correct statements regarding the congruent triangles are given as follows:

Congruent triangles are triangles in which the outer side lengths have the same measure.

Then the triangles ABC and triangle MNO are congruent by a sequence of rotations and translations, as both are right triangles.

Triangle JKL and triangle ABC are congruent by a single rotation, as the distances between the vertices of each triangle are equal.

The problem is given by the image shown at the end of the answer.

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When a number is first increased by 25% then if it is decreased by 25% , we will get the same starting number. hence the net increased or decreased value is zero.

A decline in net income is a change from one period to the next in the amount of money you have after deducting your expenses from your revenues.

There are two possible outcomes for net income. Your business has a positive net income when revenues exceed expenses. You have a negative net income, commonly referred to as a net loss, if all of your expenses exceed all of your revenues.

let the number is x

first it is increased by 25%

so,

x+(25/100)x=(125/100)x

now according to second condition,

we have to find a value by which it is decreased so we get the same number.

so, let that decreased value is y;

(125/100)x-y=x

-y=x-(125/100)x

-y=-(25/100)x

cancelation of sign;

y=25%

so this is our required value.

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A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.

Based on the plot the profits of each month can be found out using a qudratic function?

The lawn care business shows diminishing returns after month 3 . So it is not a viable business to conitnue for the long term. Based on the projections around month 8 profit becomes -$14.44. This is loss.

The other two businesses are profitable. The show upward growing trend as the months progress. Following table shows projected earnings for 1 year based on the equations showed in the graph.

3. A quadratic funtion can be used to represent the profits. The equation is given in the plots

4. A value of lawn care is negetive because the profits are decreasing after month-3. So it is sloping downards. Had the profits been raising the a-value would have been positive.

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Answer:

C

Step-by-step explanation:

Pick point 7    and sub into the equations

 eq 1    not equal to 10

 eq 2    not equal to 12

 eq 3     is equal to 15

 eq 4     not equal to 18

Now sub in the value of  -3 into equation 3     Yes equal to 15  

  so answer is   eq 3

       numbers greater than 7   and less than -3 are also true ....

The value of u is 21.

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

Given:

DG=FG=7, m ∠DEG=u+21°, and m ∠FEG=2u,

As, from the Diagram

DE = FE  (Given)

DG= FG  ( Given)

GE= GE (Common)

So, ΔDEG ≅ ΔFEG by SSS Rule.

<DEG = <FEG (CPCT)

u + 21 = 2u

2u - u= 21

u=21

Hence, the value of u is 21.

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Answer:

4/15

Step-by-step explanation:

reciprocal of 1/3 then cross multiply

Answer:

11x

Step-by-step explanation:

An example of an exponential function is the growth of bacteria. the growth of the bacteria is by exponential growth in the number of cells in a specimen of bacteria doubles every hour.

Some bacteria double her size every hour. Starting with 1 bacterium, every hour he doubles, after x hours he doubles as bacterium. This can be written as f(x) = 2x.

Bacteria replicate by binary fission, the process by which one bacterium divides into two. Bacteria therefore multiply in number by a geometric progression, doubling the population with each generation. The binary fission is the actual multiplication procedure of the cells division where cells grows fastly and further divided itself into other groups or colony.

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Answer:

f(-4)=1

Step-by-step explanation:

f(x) = 2x² + 3x - 19

f(-4)=2(-4)² + 3(-4)-19

f(-4)=2(-16)+3(-4)-19

f(-4)=-32+3(-4)-19

f(-4)=32-12-19

f(-4)=20-19

f(-4)=1

Answer: [tex]y-1=-\frac{1}{2}(x-4)[/tex]

Step-by-step explanation:

The equation of the given line can be rearranged as [tex]y=2x-4[/tex].

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we need to find is -1/2.

Using point-slope form, the equation is [tex]y-1=-\frac{1}{2}(x-4)[/tex].

Volunteer/voluntary response bias, also known as self-selection bias, occurs when research participants exert control over the decision to engage in the study.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

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Number of nails to finish the project by buying are required = 2964 units

1 package of nails contains per unit  = 52 units

To find the no. of packages we have to simply divide the total no. of nails required by the total of no. of nails of unit given in the one package of nails.

So,

Number of package required to the builder

= Total number of nails required to buy by the builder / no. of nails provided  per package

=2964/52

=57 packages

Therefore, No. of packages required by the builder to buy to complete the project

=57 packages needed.

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Answer: 57

Step-by-step explanation:

Just plug it into a calculator.

2964/52 = 57

He needs to buy 57 packages

Size will be 37 L x 15 W.

Perimeter is the distance around the edge of a shape. Discover how to calculate a shape's perimeter by adding its side lengths.

Finding the dimension is required, if the perimeter is 104 meters and the length is 7 meters longer than twice the  breadth.

Let L be the length and W be the width

L = 7 + 2*W

P = 2(L + W) ; 104 = 2(7 + 2W + W) ; 104 = 2(7 + 3W) ;

104 = 14 + 6W

6*W = 90 ;

W = 15 L = 37

Hence the dimension is 37*15

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The  value of inserting area of an array is 0.02

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

The region that an object's shape defines as its area. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area.

Given:

5 column (hundred grid) = 5/100 = 0.05

4 row (hundred grid) = 4/100 = 0.04

Find:

Area equation

Computation:

Area equation = 0.05 x 0.04

0.05 x 0.04 = 0.002

Therefore the  value of inserting area of an array is 0.02

The complete question is : Which product is represented by the model? A hundred grid model shows 5 columns shaded and 4 rows shaded. The intersecting area is an array that is 5 by 4. A. 0 . 05 × 0 . 04 = 0 . 002 B. 5 × 0 . 4 = 2 C. 0 . 5 × 0 . 4 = 0 . 2 D. 0 . 5 × 0 . 04 = 0 . 02

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Answer:

To find the dimensions of the fish tank, we can set up the equation:

(width) * (length) * (height) = 1440 cubic inches

Substituting the given expressions for the dimensions of the tank, we get:

(w) * (w + 8) * (18 - w) = 1440

This is a quadratic equation in w, and we can solve it using the quadratic formula:

w = (-(w + 8) +/- sqrt((w + 8)^2 - 4*(18 - w)11440)) / (2*1)

This simplifies to:

w = (-(w + 8) +/- sqrt(w^2 + 16w + 64 - 72w + 5760)) / 2

= (-(w + 8) +/- sqrt(w^2 - 56w + 5760)) / 2

We can further simplify this equation by factoring:

w = (-(w + 8) +/- sqrt((w - 40)(w - 144))) / 2

We can then solve for w by setting each factor equal to zero:

w - 40 = 0 => w = 40

w - 144 = 0 => w = 144

Since the width of the fish tank must be greater than 6 inches, the only valid solution for w is 40 inches. Substituting this value back into the equation for the volume of the tank, we find that the length of the tank is 48 inches (w + 8 = 40 + 8 = 48) and the height of the tank is 12 inches (18 - w = 18 - 40 = 12).

Therefore, the dimensions of the fish tank are:

width: 40 inches

length: 48 inches

height: 12 inches

The correct answer is therefore (a) width: 12 in., length: 20 in., height: 6 in.

Step-by-step explanation:

Answer: No solution

Step-by-step explanation:

3(2x + 3) - 3x = 9 + 3x

6x + 3 - 3x = 9 + 3x - 3x

6x + 3 - 6x = 9

3 = 9

No solution

Answer:

Step-by-step explanation:

To find the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly, we can use the formula:

compound interest = principal * (1 + rate/n)^(n*t) - principal

where "principal" is the initial amount of money, "rate" is the annual interest rate, "n" is the number of times the interest is compounded per year, and "t" is the number of years.

Plugging in the given values, we get:

compound interest = $50,000 * (1 + 0.064/4)^(4*10) - $50,000

= $50,000 * (1.016)^40 - $50,000

= $50,000 * 2.6335 - $50,000

= $78,167.50 - $50,000

= $28,167.50

Therefore, the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly is $28,167.50.

Answer:

Step-by-step explanation:

Therefore, the probability that their hospital stay is from 5 to 6 days is 0.03310 .

Probability deals with calculating or making estimates of how probable or "possible" an event is to occur. To convey the probability of an event occurring, words like "certainly," "impossible," or "likely" might be employed. Probabilities are always represented in mathematics as fractional, decimals, or percentages, with values that range from 0 to 1.

Here,

Given:

Mean, μ =7.37 days

Standard Deviation, σ =  2.75 days

Given: hospital stays are distributed in a bell-shaped manner, which is a typical distribution.

Formula:

Z = [tex]\frac{x-u}{\alpha }[/tex]

a) P( 5 to 6 days are spent in the hospital.)

P(5≤x≤6)

=>P([tex]\frac{5-7.37}{2.75}[/tex] ≤x≤ [tex]\frac{6-7.37}{2.75}[/tex])

=>P(-0.861≤x≤-0.498)

=>P(Z≤-0.498) - P(Z<-0.861)

=>0.034 - 0.001 = 0.03310

=> P(5≤x≤6) =3.3%

Therefore the probability that their hospital stay is from 5 to 6 days is 3.3%.

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These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.

These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.

A linear model is applicable if we can create a linear equation based on the connection between the independent and dependent variables (because there is no constant rate of change).

Otherwise, we can simulate the relationship using an exponential model.

An exponential model is:When the rate of increase representing the relationship between the year and stock price is proportional or constant, we utilize the exponential model.

By determining whether the ratio of the dependent values is the same, one can choose to describe the connection as an exponential equation.

As a result, even though the time and price scatterplot is curved, a linear model is adequate.

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The missing number in the equation 1/2 of 30 = 1/4 is 60

From the question, we have the following parameters that can be used in our computation:

1/2 of 30 = 1/4

This equation can be properly expressed as

1/2 of 30 = 1/4 of __

Represent the blank with a variable x

So, we have the following representation

1/2 of 30 = 1/4 of x

Express as products

1/2 * 30 = 1/4 * x

Multiply both sides by 4

This gives

x = 4 * 1/2 * 30

Evaluate

x = 60

Hence, the missing number is 60

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Answer:

[tex]\huge{\boxed{82.8\text{ units}}}[/tex]

Step-by-step explanation:

Because the triangles have all of the same angles, similarity can be proven via AAA.

Now that ΔJKL ~ ΔMNO, the sides must be proportional.

Because the sides are proportional, the following equation can be made:

[tex]\frac{24}{20}=\frac{x}{22}[/tex]

Via cross-multiplication, the equation simplifies to:

20x = 24 * 22

20x = 528

x = 26.4

Now, because perimeter is simple the sum of all sides, the perimeter of ΔMNO is simply 32.4 + 24 + 26.4, or 82.8.

Hope it helps :) and let me know if you want me to elaborate.

Answer:

(-3.25,3.75)

Step-by-step explanation:

Thuis can be answered with either of two approaches:  Graphing and Matematical.  We'll do both:

Graphing

Graph both equations.  It is helpful to use a free online graphing utility:  DESMOS.

The attached graph reveals the intersection of the lines at point (-3.25, 3.75).

Matematical

Solve the equations be using substitution.  Rearrange either equation to isolate one of the two variables (x or y).

Lets use the second, since y is already isolated, making the task simple and fast.  But the other equation could also be used, if desired.

y=x+7

Now use this expression of y in the other equation:

9x+3y=-18

9x+3(x+7)=-18

9x +3x +21 = -18

12x = -39

x = -(39/12)

x = -3 - (3/12)

x = -3.25

Now use x= -3.25 in either equation tand solve for y:

y=x+7

y=(-3.25)+7

y = 3.75

The solution to this series of equations is (-3.25,3.75)

The total area of the two shaded faces of the cuboid below is = 112[tex]cm^{2}[/tex]

Since the two shaded faces of the cuboid shown are adjutant to each other and are of the same dimensions so according to the calculations -

Let us consider only one side of the shaded portion-

The length of the shaded part = 8cm

The width of the shaded portion = 7cm

So it appears that due to the uneven measure of length and breath this is a rectangle, so the area of a rectangle

= [ length (l) x width(w) ]

= 8cm x 7cm

= 56[tex]cm^{2}[/tex]

Since the question asks the total area of both sides so because both the shaded sides are equal then total area = 56 x 2 = 112    [tex]cm^{2}[/tex]

Therefore, the total area of the shaded faces of the cuboid = 112[tex]cm^{2}[/tex]

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4 is the value of w which makes the equation true.

What is an equation?

It is given that,

3(−4w−5)=−7(5+w)

by solving the equation,

-12w-15=-35-7w

12w-7w=35-15

5w=20

w=20/5

∴w=4

Hence, 4 is the value of w which makes the equation true.

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Answer:

1.) x = 1, 2/3  

2.) x = -3±[tex]\sqrt{6}[/tex]

3.) x = [tex]\frac{4+/-\sqrt{37} }{3}[/tex]  or x = −3.36092084, 0.69425417

Step-by-step explanation:

These are quadratic equations so we use the quadratic formula method.

Use the quadratic formula by taking:

[tex]ax^{2}+bx^{2} +c=0[/tex]

1.) a = 3, b = -5, c = 2

2.) a = 1, b = 6, c = 3

3.) a = -3, b = -8, c = 7

Then, substitute into the quadratic formula:

(Check the picture provided for the quadratic formula)

Answer:Calcula el número si 30 menos el triple del número es cuatro veces la diferencia del triple del número más 10

Step-by-step explanation: